Tez özetleri Astronomi ve Uzay Bilimleri Anabilim Dalı

A Study Of Modular Multıplıcatıon Algorıthms And Theır Applıcatıons In Cyrptography

In this study, modular multiplication operation that is one of the main operations of crypto-systems which are used for security purposes. In the literature, five different iteractive modular multiplication algorithms that has been developed in the last few years, is analyzed and the simulation programs that are developed and performances are acquired. In order to compare and contrast of methods with each other, common performance criteria like duration of algorithm delay, addition operation counts, memory size, and iteration counts are chosen. Simulation results that are attained and analytical results are demonstrated on the common performance graphics. In addition, iterative multiplication algorithms are applied on the RSA crypto-system, performances of methods are reevaluated, the correctness of the results acquired are tested.

In the “General Background” section, modular multiplication operation and classification of the used methods are considered. In this manner, it is identified that it can be divided into two main class like Blackley (iterative method) and Montgomery method, and their general properties and comparisons are given. Also, in this section main information about number systems and RSA crypto-system that is chosen as application exists.

In the “Methods” section, detailed information about iterative modular multiplication algorithms in the recent years are given.

In the “Results” section, perfomance analysis realized with the help of simulation programs written in Turbo C language prepared with algorithms mentioned in “Methods” section are given. Comparison of methods according to performance criteria selected for this purpose are obtained both analytically and by means of simulation results. In this section, an RSA crypto system taking text characters as message input is generated and retesting of methods is provided with the application of examined iterative algorithms over the system.

In the “Conclusion” section, evaluation of all the results obtained in the thesis and advisory information about possible future studies that researchers could make also take place. In conclusion, consistency of examined iterative multiplication methods, performance analysis done, and results of analyticand simulations are identified.

ARAS Pelin ,

Danışman : Yrd. Doç. Dr. Oğuzhan ÖZTAŞ

Anabilim Dalı : Bilgisayar Mühendisliği

Mezuniyet Yılı : 2006

Tez Savunma Jürisi : Yrd. Doç. Dr. Oğuzhan ÖZTAŞ (Danışman)

Doç.Dr. Sabri ARIK

Prof. Dr. Ahmet SERTBAŞ

Prof. Dr. Mahmut ÜN

Doç. Dr. Hakan Ali ÇIRPAN